A Class of Tests Based Jointly on Sub-Sample Minimum and Median

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

In Statistics, nonparametric tests play a very important role when the data sets are not normal. In this paper, we develop a class of nonparametric tests to compare location parameters of two populations. The proposed test statistic is based jointly on minimum and median of the sub-samples. The mean and variance of the test statistic are derived. The test statistic has asymptotic normality under some assumptions. The proposed class of the tests is compared with its existing competitor’s w.r.t. Pitman and Bahadur asymptotic relative efficiency. As an illustration, the proposed test is applied to a real life data set. We carried out the Monte Carlo simulation study to find the power and level of significance of the proposed test.